This invention relates to an improved technique and apparatus for forming holes in thin sheet stock, such as plastic sheet of the order of a few mils thickness and, particularly to improvements in the formation of relatively large holes therein. For example, it often is desirable to form large holes to define a handle in bags made from thin sheet material such as polyethylene. Such bags have received increasing acceptance in recent years and are now in substantially wide spread use in a variety of environments. Because of the thin and highly flexible nature of the sheet material from which the bag is made, punching of such larger holes presents a number of difficulties which are not normally encountered in the punching of relatively small holes (e.g., for ventilation). One of these difficulties results from the fact that when punching a relatively large hole, the slug portion is not always completely and cleanly severed and may remain partly attached to the bag. This results from the fact that as the punching out of the slug progresses, the highly flexible nature of the thin sheet material enables the slug to be drawn along with the punch. The slug thus is not maintained in its intended substantially flat attitude as is desired at all times during the punching operation. In addition, failure to retain the slug portion of the sheet in a flat configuration during the punching operation may also result in an irregularly shaped hole even if the slug is completely severed from the sheet. It is among the primary objects of the invention to provide an improved apparatus and technique for punching such enlarged holes in thin, flexible sheet material while avoiding the foregoing and other difficulties.